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Ve216LectureNotesChapter1Part1

# Ve216LectureNotesChapter1Part1 - Ve216 LECTURE NOTES...

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Ve216 LECTURE NOTES Dianguang Ma Spring 2009

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Course Information Code: Ve216 Credits: 4 Prerequisite: Applied Calculus Required Textbook: Signals and Systems, 2/e, by Simon Haykin and Barry Van Veen, Wiley, 0471-37851-8. Lecturer: Dianguang MA TA: Hao WANG
Course Information Office Hours: All Tuesdays, Thursdays, and Fridays, 12:00-13:00, Law School Building, Room 213

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Course Information Topics Introduction (Chapter 1) Time-Domain Representations of Linear Time- Invariant Systems (Chapter 2) Fourier Representations of Signals and Linear Time- Invariant Systems (Chapter 3) Applications of Fourier Representations to Mixed Signal Classes (Chapter 4) Representing Signals by Using Continuous-Time Complex Exponentials: the Laplace Transform (Chapter 6) Representing Signals by Using Discrete-Time Complex Exponentials: the z-Transform (Chapter 7)
Course Information Grading Nine Problem Sets: 10% Three Matlab Labs: 15% Three Exams Exam 1: 20% Exam 2: 25% Exam 3: 30%

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1.1 What Is a Signal? A signal is formally defined as a function of one or more variables that conveys information on the nature of a physical phenomenon. When the function depends on a single variable, the signal is said to be one dimensional . When the function depends on two or more variables, the signal is said to be multidimensional .
Recall: Relations and Functions A relation is a set of ordered pairs. Example: The parks and Recreation Board suspects that the number of people who go to White Sands Beach on any given day depends on the temperature on that day. The following summarizes some of the data collected over on summer and it can be described with ordered pairs {(60, 27), (70, 94), (75, 138), (80, 221), (85, 347), (90, 462)}. The first coordinate of each pair is the temperature, and the second coordinate is the number of people at the beach. This set is an example of relation.

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Recall: Relations and Functions The set of all first coordinates is the domain of the relation, and the set of all second coordinates is the range of the relation. A function is a relation in which no two ordered pairs have the same first coordinate. Alternative definition of a function: A function x ( t ) is a rule that assigns any permissible value of the variable t to a unique value x . The domain is the set of all permissible values of t .
1.2 What Is a System? A system is formally defined as an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals. Alternative definition of a system: A system can be viewed as a process in which input signals are transformed by the system or cause the system to response in some way, resulting some signals as outputs.

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Figure 1.1 (p. 2) Block diagram representation of a system.
1.3 Overview of Specific Systems A simple system: a resistor A complex system: a communication system

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1.4 Classification of Signals Five methods of classifying signals, based on different features, are common: Continuous-time and discrete-time signals Even and odd signals Periodic and nonperiodic/aperiodic signals Deterministic and random signals Energy and power signals
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